Cluster expansion for the Ising model in the canonical ensemble

TL;DR

This paper proves the validity of the cluster expansion for the Ising model in the canonical ensemble, providing insights into decay of correlations, CLT, and large deviations, and compares convergence bounds with the grand-canonical ensemble.

Contribution

It establishes the cluster expansion in the canonical ensemble for the Ising model and quantifies error terms for key statistical properties.

Findings

Cluster expansion is valid in the canonical ensemble.

Convergence bounds are compared with grand-canonical results.

Quantitative error estimates for correlations and large deviations.

Abstract

We show the validity of the cluster expansion in the canonical ensemble for the Ising model. We compare the lower bound of its radius of convergence with the one computed by the virial expansion working in the grand-canonical ensemble. Using the cluster expansion we give direct proofs with quantification of the higher order error terms for the decay of correlations, central limit theorem and large deviations.